Fig. 3

Summary of sensitivity analyses for the smallest bistable system (a) Eigenvalue sensitivity \({\hat{m}}\) for stable state 1 and 2 (\(SS_1\), \(SS_2\)), with parameter perturbations for \(k_1\) through \(k_4\). For \(SS_1\) (0, 0) the maximum eigenvalue is influenced only by \(k_4\); \(k_1\), \(k_2\), and \(k_3\) do not influence it (shown by the zero eigenvalue sensitivity). For \(SS_2\) (6, 4.5), \(k_1\) and \(k_2\) perturbations in the positive direction stabilize it while a similar change in \(k_3\) and \(k_4\) destabilizes it. (b) Sensitivity of separation between stable steady states for the system. Parameter \(k_1\) has minimal effect on the goodness of this switch. When perturbed in the positive direction, parameter \(k_2\) increases the separation between \(SS_1\) and \(SS_2\). Parameters \(k_3\) and \(k_4\) both need to be perturbed in the negative direction to increase separation, \(k_3\) having the largest influence. For a simple system such as the one investigated here, these trends are visually evident in the one-parameter bifurcation curves in Fig. 1d